1. [-/12.5 Points] DETAILS HARMATHAP12 14.3.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The cost (in dollars) of manufacturing one item is given by C (x, y) = 20 + 2x + 8y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. (a) If the hourly cost of labor is $20, and the material costs $8 per pound, what is the cost of manufacturing one of these items? $ (b) Find the partial derivative of C with respect to x. CX = Interpret the partial derivative of C with respect to x. O The cost (in dollars) of manufacturing one item will increase by $8 for a $1 increase in y if x is held constant. The cost (in dollars) of manufacturing one item will increase by $2 for a $1 increase in x if y is held constant. The cost (in dollars) of manufacturing one item will increase by $20 for a $1 increase in x if y is held constant. The cost (in dollars) of manufacturing one item will increase by $2 for a $1 increase in y if x is held constant. The cost (in dollars) of manufacturing one item will increase by $8 for a $1 increase in x if y is held constant. Need Help? Read It Watch It 2. [-/12.5 Points] DETAILS HARMATHAP12 14.3.003.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The total cost of producing 1 unit of a product is C(x, y) = 38 + 6x + 2y +- dollars 46 where x is the cost per pound of raw materials and y is the cost per hour of labor. (a) If labor costs are held constant, find the function that describes the rate at which total cost increases for each increase of $1 per pound in material cost. (b) If material costs are held constant, find the function that describes the rate at which total cost increases for each $1 per hour increase in labor costs. Need Help? Read It Master It 3. [-/12.5 Points] DETAILS HARMATHAP12 14.3.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The joint cost (in dollars) for two products is given by C (x, y) = 25 + x2 + 3y +2xy where x represents the quantity of product X produced and y represents the quantity of product Y produced. (a) Find the marginal cost with respect to x if 5 units of product X and 12 units of product Y are produced. $ Interpret your answer. O If y remains at 12, the expected change in cost for a 6th unit of x is this amount. If x remains at 5, the expected change in cost for a 13th unit of y is this amount. If y remains at 5, the expected change in cost for a 13th unit of x is this amount. If x remains at 12, the expected change in cost for a 6th unit of y is this amount. (b) Find the marginal cost with respect to y if 5 units of product X and 12 units of product Y are produced. $ Interpret your answer. O If x remains at 12, the expected change in cost for a 6th unit of y is this amount. O If y remains at 5, the expected change in cost for a 13th unit of x is this amount. If y remains at 12, the expected change in cost for a 6th unit of x is this amount. O If x remains at 5, the expected change in cost for a 13th unit of y is this amount. Need Help? Read It8. [412.5 Points] DETAILS HARMATHAP12 14.3.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The demand functions for (3,; and '75 units of two related products, A and B, are given. Assume pA and p3 are in dollars. {GA = 325 5.0.4 4P3 q5 = 200 BpA 9p3 (a) Find the marginal demand of qA with respect to pA. (b) Find the marginal demand of CIA with respect to p5. (c) Find the marginal demand of qB with respect to p5. (d) Find the marginal demand of as with respect to pA. (e) Are the two goods competitive or complementary? 0 They are competitive. O They are complementary. Need Help